OPTIMAL CONTROL THEORY FOR DISTRIBUTED PARAMETER PROCESSES BASED ON INTEGRAL EQUATION REPRESENTATIONS

Conventional optimal control theory for distributed parameter systems is usually based on partial differential equation representations. In this thesis, this subject is also considered and a set of necessary conditions in the form of various maximum principles is derived. The derivation and the proof of the maximum principles are carried out rigorously and, therefore, the results constitute a new development in the optimal control theory for distributed parameter systems. The main subject, however, is the rigorous development, derivation and proof of various maximum principles for a general class of nonlinear distributed parameter control systems based on integral equation representations. The weak solution theory developed by Fucik and Kufner for nonlinear partial differential equations is used in the development and derivation. In this new development, two main limitations of Butkovskiy's maximum principle have been eliminated.;The optimality conditions for a class of Robin problems (the boundary conditions of the third kind) are also developed. The method of weak solution developed by Fucik and Kufner is again used to handle nonlinearities in the differential operators as well as in the nonhomogeneous terms, leading to the development of a new set of optimality conditions.;An imbedding method of converting a two-point boundary value problem into an initial value problem to overcome cumbersome numerical computations in the synthesis of optimal control is also treated.;Finally, the possible control strategies in computations coupled with the various maximum principles and techniques developed in the thesis are systematically explored and discussed. The differences and some relationships between various strategies for synthesizing optimal control are elucidated.;Application examples in the control of chemical engineering processes are then presented. The numerical computations in the examples demonstrate that the new maximum principles based on integral equation representations are easier to programme and are more flexible and yet require considerably less computing time than for the conventional type maximum principles based either on differential equation representation or on Butkovskiy's integral equation representation.